Loss Given Default (LGD) Calculator
From exposure at default and recovery value, compute the loss given default rate of a loan/credit asset.
Input Data
Results
At a glance:Loss Given Default (LGD) is the loss rate after default — the unrecovered portion of exposure after realising collateral: LGD = (EAD − RV) ÷ EAD × 100% = 1 − RV/EAD. EAD = amount owed at default; RV = recovered value after collateral sale/guarantee. Example EAD 1,000,000, recovered 400,000 → LGD 60%. LGD is the 'severity' of credit risk; with PD and EAD, expected loss = PD × LGD × EAD. It underpins bank capital and credit pricing.
Formula
LGD = (EAD − RV) ÷ EAD × 100%.
Equivalently LGD = 1 − (RV ÷ EAD).
Expected loss = PD × LGD × EAD.
$$LGD = \dfrac{EAD - RV}{EAD} \times 100\%$$$$\text{Expected Loss} = PD \times LGD \times EAD$$How to Use
- Enter the exposure at default (EAD).
- Enter the recovery value recovered after default.
- View the LGD rate (0 to 1).
EAD HK$1,000,000 — LGD by recovery value
| Recovery value | Loss | LGD |
|---|---|---|
| 800,000 | 200,000 | 20% |
| 500,000 | 500,000 | 50% |
| 300,000 | 700,000 | 70% |
| 0 | 1,000,000 | 100% |
LGD = (EAD − RV) ÷ EAD × 100%. Higher recovery → lower LGD. With zero collateral recovery, LGD reaches 100% (total loss).
Case Studies
Case 1: LGD with mortgage collateral
A loan of HK$1,000,000 defaults; the bank sells the mortgaged property for HK$800,000 (after costs) — recovery HK$800,000.
LGD = (1,000,000 − 800,000) ÷ 1,000,000 = 20%. With solid collateral, loss is only a fifth — collateral sharply lowers LGD.
Contrast: an unsecured personal loan of the same HK$1,000,000 defaulting with no recovery → LGD 100%, full loss. This is why secured loans price lower than unsecured.
Case 2: LGD drives expected loss with PD
Two loans both EAD 1,000,000; PD 5%. A: LGD 20% (secured) → expected loss = 5% × 20% × 1,000,000 = HK$10,000. B: LGD 80% (weak collateral) → expected loss = 5% × 80% × 1,000,000 = HK$40,000 — 4× higher.
Same default chance, vastly different loss because of LGD. Banks set provisions, capital and pricing by PD×LGD×EAD; weak collateral/legal recovery pushes up LGD, raising capital and rate.
Practical notes: (1) banks also use downturn LGD (collateral value in stress, haircuts, legal/time costs) — higher than normal LGD; (2) recovery timing and discounting matter (recovery in 3 years is worth less); (3) guarantees/insurance lower effective LGD. Educational/estimation only.
FAQ
What is LGD and how is it computed?
LGD is the loss rate after a borrower defaults — the unrecovered share of exposure: LGD = (EAD − RV) ÷ EAD × 100% = 1 − RV/EAD. EAD = amount owed at default; RV = recovered value after collateral/guarantee. Example EAD 1,000,000, recovered 400,000 → LGD 60% — you lose 60% of the principal even after recovery.
How does LGD relate to PD and expected loss?
PD = probability of default (chance), LGD = loss given default (severity), EAD = exposure. Expected loss = PD × LGD × EAD. Same PD but higher LGD (weaker collateral) → far higher expected loss; banks size provisions, capital and pricing by this triple.
Why do secured loans cost less?
Because collateral raises recovery (RV), lowering LGD, so expected loss is smaller; banks need less capital and charge a lower rate. Unsecured loans (LGD up to 100%) carry higher pricing.
What lowers LGD in practice?
Mainly: (1) collateral/guarantee — real estate, deposits, third-party guarantees or insurance raise recovery; (2) seniority — senior debt recovers before junior; (3) short tenor/liquidity — easier to realise; (4) strong legal recovery — quick, low-cost enforcement; (5) haircuts and costs — collateral value and legal/time costs directly hit recovery, so value and enforcement matter. So lenders rely on collateral, guarantees, covenants and legal strength to cut LGD; stressed/weak collateral raises it (banks use downturn LGD). Educational/estimation only.
What is the difference between LGD and EAD?
Both are credit-risk components but answer different questions. LGD = loss given default — the percentage of exposure lost after default (severity, 0–100%), depending on collateral/guarantee/recovery. EAD = exposure at default — the amount owed at default (the loss base, in money). They combine with PD: expected loss = PD × LGD × EAD. Example: a HK$1,000,000 loan, PD 5%, LGD 60% → expected loss = 5% × 60% × 1,000,000 = HK$30,000. PD is the chance of default, EAD the exposure size, LGD the loss rate if defaulted — three dimensions of credit risk. Banks estimate all three for provisioning, capital and pricing.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.